Heterogeneous responses in Google Trends measures of well-being to the COVID-19 dynamic quarantines in Chile

We study how the Chilean population’s well-being responded to the strategy implemented by their health authorities, known as Dynamic Quarantine, to contain the spread of coronavirus in which municipalities periodically entered and exited lockdowns. This unique scheme, together with the population’s socioeconomic heterogeneity, facilitates the estimation of changes in this well-being as differentiated by socioeconomic status. Using Google Trends to compute measures of well-being, we find strong evidence that socioeconomic status induces heterogeneity in these changes; thus, neglecting this heterogeneity may lead to misleading prescriptions for the public policy that addresses the psychological effects of lockdowns.

. Estimation strategy. The diagram represents the length and timing of lockdowns under the Chilean Dynamic Quarantine scheme. Wealthy and non-wealthy municipalities are represented by different colors. Calendar time is on the horizontal axis and the length of the boxes for each municipality represents the duration of the lockdowns. The beginning or end of a lockdown need not be similar among municipalities. DiD refers to "difference-in-differences".

Methods
Measuring well-being. Our measure of well-being is based on GT searches. As described in Scott and Varian 13 , GT is a service that produces time series data on search volume intensity (SVI) to measure the popularity of a particular keyword in a specific period and location. The SVI is measured on a scale that ranges from 0 to 100, where the value of 100 indicates the peak of popularity and 0 indicates complete disinterest. GT may qualify analyzed phrases as either a search term or a topic. Search terms are literally typed words, while topics may be proposed by GT when the tool recognizes phrases related to popular queries. While collecting data, values below 1, denoted as " < 1 ", were replaced by 1. We specify the region as CL (Chile). We Google search for nine well-being and mental health related topics for the months from March 2020 to July 2020 and for the same months in 2019. These topics, presented in Table 1, were taken from Brodeur et al. 5 who in turn choose topics that are as close as possible to the different items in the General Health Questionnaire 24,25 . A growing number of studies in psychology have explored the psychological effect of lockdowns and personal quarantines during the COVID-19 outbreak. Their list of words on psychological effects resembles our list of topics 8,9,[26][27][28][29] . Since the actual searches were made in Spanish, we provide the 87 Spanish keywords that are associated with these topics in the second column of Table 1. As a reference, we present these keywords in English in the third column of the same table.
The SVI of the proposed keywords are aggregated by taking the average across all individual keywords within a topic for each day t to obtain an average search volume intensity, ASVI t . The higher the value of the ASVI, the greater the population's attention to that topic on a specific day. Then, we follow the work of Da et al. 30 by using the abnormal search volume activity (ASVA) as our proxy for the well-being of the population. The ASVA is defined as: where ln(.) denotes the natural logarithm, and ASVI * t is computed as the monthly average of the corresponding ASVI during the corresponding month in 2019. Thus, the ASVA is the log-percent deviation in the current search volume intensity from a reference value in a normal year. Table 2 presents the descriptive statistics for the ASVA that we computed between January and August, 2020. We also include the descriptive statistics for the COVID-19 reproductive number R 0 that is used later in our empirical specifications to control for the general conditions of the pandemic.
Lockdowns and socioeconomic status. The Chilean Dynamic Quarantine has very peculiar characteristics which have already attracted the interest of researchers 10,31,32 . There are two distinct stages in the Chilean strategy. In the early stage, which corresponds to the period between March 24th and July 20th, 2020, the government imposed complete lockdowns in different municipalities according to their pandemic situation. In the second stage, the so-called step by step plan, the government changed its strategy to ease the complete lockdowns imposed up to that point by implementing restrictions based on five stages or incremental steps that ranged from lockdown to advanced opening. We restrict our attention to the first stage in which the health authorities made a total of 25 weekly announcements (available at www. minsal. cl) about which municipalities nationwide would be under lockdown during the following week.
We consider the lockdown situations of municipalities with a population larger than 13,000 people. This sample covers 120 municipalities that represent approximately 83% of the country's total population (14.5 million people). The descriptive statistics for the number of lockdowns and for the number of days in their duration are presented in Table 3. As a proxy for the SES of the population, we use the poverty index (PI) reported by the Ministry of Social Development (Ministerio de Desarrollo Social y Familia) in the CASEN 2017 household Effects on well-being. Next, we describe the framework for our empirical analysis to study the effects of lockdowns on the well-being of the population, as measured by the ASVA index, and their heterogeneity across municipalities classified by wealth. Such effects can be consistently estimated in a linear equation with interactions in what is known as a difference-in-differences (DiD) estimation [33][34][35][36][37] . To be more precise, the nature of the dynamic lockdown scheme means different treatment timing for different municipalities. This setup corresponds to a staggered DiD model that is similar to the event study method that uses event time (number of days since the announcement of a lockdown) rather than calendar time 38,39 . However, in our empirical framework, the dependent variable, ASVA, is already a difference between the volume of searches between day t and an historical average; thus, the estimation we entertain is actually a triple difference estimation -DiDiD (time, lockdown status, and wealth) 40,41 .
Municipalities are the smallest administrative unit in Chile and, geographically, they constitute a finer partition than is covered by GT. In other words, for each day t in our sample period, we observe the same value of the ASVA for all municipalities. We discuss the conditions under which the effects of interest, and their heterogeneity across municipalities, can be estimated consistently despite this measurement particularity.

Effects of interest.
Let i index municipality, t index calendar time, and τ be a counter of the number of days since the announcement of the last lockdown. Further, the τ resets to zero when the end of the lockdown if finally announced. Given the dynamic nature of the Chilean lockdown strategy, τ depends on t but to alleviate the notation we leave that dependence implicit.
We define a dummy variable D it (τ ) such that D it (τ ) = 1 if municipality i at time t has been locked down for τ periods (i.e., if municipality i is locked down at time t, a condition that was announced at calendar time t − τ ),  www.nature.com/scientificreports/ and D it (τ ) = 0 otherwise. Let Y it be the ASVA for a given topic or search term related to some dimension of well-being in municipality i at time t. Then, we have: that is the average effect of a lockdown on the well-being after τ periods for the population in any Chilean municipality. Thus, the profile {�(1), �(2), ..., �(m)} is of interest to track the evolution of such effects as the lockdown continues over m periods. Let W i be a municipality-specific dummy variable such that W i = 1 if municipality i is wealthy, and W i = 0 if it is not. This dummy variable is not time varying since we do not expect a change in the socioeconomic status of municipalities in the relatively short time span of our sample. Then, for k = {0, 1} , we define: as the average effect of a lockdown, after τ periods, on the well-being measure of the inhabitants of a wealthy (k = 1) or a non-wealthy (k = 0) municipality. We define: as the differentiated lockdown effect on well-being in a wealthy municipality relative to that in a non-wealthy one. While �(τ ) in (2) has an effect on the average municipality, � 10 (τ ) in (3) indicates if such an effect depends on the socioeconomic status. Thus, the profile {� 10 (1), � 10 (2), . . . , � 10 (m)} is of interest to study whether the lockdown produces this gap over m periods.
Let p = Pr(W i = 1) be the proportion of wealthy municipalities in Chile at the time of the pandemic. Then, the average effect of a lockdown on well-being in the population can be written as: which relates the effects on subpopulations with the aggregate. Moreover, even though �(τ ) can be identified from the data under mild conditions, the requirements to identify � 10 (τ ) are more stringent; thus, the decomposition in (5) is not generally feasible. In fact, �(τ ) can be computed from time variation, that is, a before-after comparison with a lockdown that treats all municipalities equally, or from cross-sectional variation as long as there are municipalities that are never affected by the lockdown. On the other hand, � 10 (τ ) requires variation in both dimensions simultaneously, which is provided by the unique Chilean quarantine design.
Regression setup. Studies have well-documented that a DiD estimation can be implemented in a linear regression model that features the treatment dummy variable and its interaction with time. Likewise, a third dimension such as SES can be introduced through further interactions 41 . Thus, the above quantities of interest can be estimated as coefficients in a linear regression, or their linear combinations, which is quite convenient for the computation of standard errors and subsequent hypothesis testing.
Consider a longitudinal sample of n municipalities over T periods, and the linear regression model: where (β τ , δ τ ) for τ = 1, 2, . . . , m are regression coefficients, α i is a municipality effect and u it is the error term. The coefficients β and δ can be estimated consistently with the so-called within-group estimator under the mild condition that E(ε it | D it (τ ) = d) = 0 for d = {0, 1} and τ = 1, 2, . . . , m or, in other words, that ε it is mean independent from D it (τ ) . This independence happens if there is no feedback from the well-being measures on the decision to declare a lockdown, which we argue to be a reasonable assumption as the related policies predate the public worries on mental health and similar considerations. Further, α i and γ i are not identified, since they are removed from the equation with the within-group transformation.
The coefficient δ τ is the effect of a lockdown on the well-being of the population in a non-wealthy municipality, and β τ is the added effect for the population in a wealthy municipality, that is, the DiDiD. Thus, from (5) and (7) the effect on the whole population is: Measurement error. The ASVA is observed at an aggregate level, not at a municipality level. Yet, it is still possible to estimate the quantities of interest. The idea is that the dependent variable is measured with an error. If the measurement error were classical (i.e., simply a noise), then the error term in the regression will increase its variance with no further consequence. In practice, the measurement error may not be classical; what is required is that it does not correlate with the policy interventions after removing time variation and municipality-specific effects.
To elaborate, consider the factor decomposition:  (10) is the feasible, error-ridden version of (6). The within-group estimation removes all influences from α i and W i , and the consistent estimation of the coefficients 1} and τ = 1, 2, . . . , m . An interpretation of this mean independence condition is that if all variation in Y it due to the effects on the lockdown and its continuation is captured by Y t , then the coefficients in (10) are exactly like those in (6). Put differently, the coefficients (β τ , δ τ ) capture the effects of a lockdown and even its heterogeneity across municipalities as classified by W i that are important enough to produce time variation in the aggregate well-being.

Results
Next, we present the results for the within-group (fixed-effect) estimates of the coefficients in equation (10), and some linear combinations, for each of the topics in Table 1. Besides the lockdown dummies and their interactions with the municipality SES dummy, the regression also includes the COVID-19 reproductive number R 0 to control for the general conditions of the pandemic, month dummies, day of the week dummies, and a first and second lockdown dummy. Standard errors are clustered at the municipal level. We consider wealthy municipalities as those that belong to the top decile according to the PI sorting, so p = 0.10 . We also consider m = 60 days, so that the effects are up to two months after the announcement of a lockdown. The interest is on the profiles {�(τ )} τ =m τ =0 , {� 0 (τ )} τ =m τ =0 , and {� 10 (τ )} τ =m τ =0 that we are able to estimate without imposing any a priori functional form of τ = 0, 1, . . . , m . Such an eclectic approach provides flexibility in the functional forms but at the cost of abundant outputs which we present concisely in Fig. 2, Tables 4, and 5. In Fig. 2 we present the estimated lockdown effect on the whole population, �(τ ) ; the lockdown effects on the non-wealthy population, δ τ ; and the DiDiD estimates, β τ for τ = 0, ..., 60 with their corresponding 95% confidence intervals and, to ease visualization, a polynomial time trend. On the other hand, in the tables we report the average estimates across τ , the proportion of periods that the effects are positive or negative, and the corresponding proportion of periods in which the effects are statistically significant (i.e., their confidence intervals do not contain zero) at various confidence levels.
Effects on the whole population. The panels to the left of Fig. 2 show �(τ ) as a function of τ for each sentiment. Our first finding is that even though the point estimates do appear to display some time variation, that is, �(τ ) behaves differently for different τ , the differences across τ are not statistically significant. That is to say, with very few exceptions and for all topics, the confidence interval of some �(τ 1 ) overlaps with that of �(τ 2 ) for τ 1 = τ 2 , which means that we will not be able to reject a null hypothesis of the type H 0 : �(τ 1 ) = �(τ 2 ).
An implication is that in most cases, the effect of an additional day in lockdown on the population's well-being is relatively constant as τ increases. It does not increase, nor does it vanish. There are some possible exceptions to this pattern: Boredom that indicates some positive and significant short-run effects within the first 20 days; Worry whose effect trend upwards and become positive and significant after a month; and Self-care whose effect is negative and significant immediately after the announcement and after the first month.
A second finding is that the signs, significances and magnitudes of the effects on the ASVA vary across topics or dimensions of well-being. Table 4 complements Fig. 2 by giving related statistics. The effects on the ASVA of Sleep and Stress are generally not significant (i.e., their confidence intervals contain zero). For Sleep, the average estimated effect is −0.06 , as nearly 28% of the estimated �(τ ) are positive, with only 6.56% being statistically significant at the 5% confidence level. For the negative ones, only 31% are statistically significant. For Stress, the average point estimate of �(τ ) is zero with 52% having positive estimated coefficients of which only 13.1% are statistically significant. The other 48% have negative coefficients of which 18% are statistically different from zero at the 5% level. The results of Boredom, Loneliness, and Worry are similar: the average effects are positive but small (0.15, 0.05, and 0.05, respectively), and the proportion of periods with point estimates that are positive ranges from 70 to 78% out of which between 40 and 51% are statistically significant at the 5% level. For Self-care and Panic, the average effects on ASVA are negative ( −0.10 and −0.18 , respectively). For these topics, the proportion of periods with negative effects are 83 and 86% of which between 50 and 65% are significant at the 5% confidence level. Finally, the effects for Frustration and Irritability are the most significant and the largest in magnitude, although they are positive for Frustration and negative for Irritability. The average effects are, respectively, 0.71 and −0.29 with more than 95% being positive or negative, respectively, of which between 81 and 84% are significant at a 5% confidence level. Socioeconomic heterogeneity. The above effects on the whole population, �(τ ) = δ τ + pβ τ , come from combining an effect on the ASVA of non-wealthy municipalities, δ τ , with a term proportional to the DiDiD estimator β τ . The parameters δ τ and β τ can be identified by the unique characteristics of the Chilean dynamic quarantine. The panels on the right of Fig. 2 and Table 5 show the results. The results on Boredom, Loneliness, Stress, Worry, and Frustration are similar in that the estimated β τ are consistently negative, although with various degrees of significance. The negative DiDiD estimates mean that the population from non-wealthy municipalities pays more attention and responds more intensively to these topics during lockdowns than the population from wealthy municipalities. Anecdotally, people in wealthy areas feel less bored, lonely, stressed, worried, and less frustrated as a response to lockdowns than inhabitants in poorer areas.
In the case of Boredom, the average β τ is −0.74 , and 98% of the coefficients are negative of which 89% are significantly different from zero at a 5% significance level. The average effect on the non-wealthy population, δ τ , is 0.22 and the effect is positive in 84% of periods, out of which 57% result significantly different from zero at the 5% level. The β τ coefficient is large enough (in absolute value) so that these figures are higher and more significant than those corresponding to the whole population (average effect of 0.15 and positive for 79% of the periods of which 51% are significant). A similar configuration is found for Worry and Frustration, but in the latter case the effects are positive and almost always significant for the whole population. For Frustration, the average β τ is −1.09 and this coefficient is significant at the 5% level for 64% of the time for 84% of periods of with negative effects. The average δ τ is 0.82 that is higher than the average �(τ ) of 0.71 but both figures are significant about 80% of the time for more than 95% of the positive effects.
The cases of Loneliness and Stress are similar in that the β τ coefficients remain significant, even though they are not large enough to noticeably affect the whole population as compared to the non-wealthy population. For www.nature.com/scientificreports/ instance, for Stress the average β τ is −0.20 ; this coefficient is negative 90% of the time of which 61% are significant at the 5% confidence level. Correspondingly, the average δ τ is close to the average �(τ ) and their confidence intervals almost always include zero. On the other hand, the results on Irritability and Sleep are comparable as the estimated β τ are mostly significant and positive, that means the population from non-wealthy municipalities respond to lockdowns less intensively in these GT searches than the population from wealthy municipalities. People in wealthy areas tend to feel more irritated and more concerned about sleep. A similar pattern arises for Self-care and Panic but in general the DiDiD estimates are not significant.
For Irritability, the average δ τ coefficients is −0.32 in which 88% have significantly negative coefficients at the 5% confidence level. The effects on the whole population are higher. The average � τ is −0.29 in which the estimated coefficients are negative 97% of the time of which 84% are significant at the 5% level. Thus, the average β τ is 0.30 which is positive 84% of the time of which 48% are significant. In the case of Sleep, the average β τ is 0.25 which is also positive 84% of the time of which 59% are significant cases.
All in all, these findings disclose important differences between wealthy and non-wealthy populations' interests in search topics on lockdowns. Furthermore, it provides evidence that the estimations of social well-being during the pandemic might be biased if SES heterogeneity is neglected.
In the estimation of equation (10), we include municipality fixed effects, month time effects, the level of R 0 , day-of-the-week dummies, and the first and second lockdown dummies. The estimation results for the R 0 and for the first and second lockdown dummies are presented in Table 6.
Regarding the R 0 , we add its level to equation (10) as a control for the general conditions of the pandemic. For most of the topics, we obtain the expected signs for this variable. The higher the R 0 is, the higher the levels Table 4. DiDiD estimation: Lockdown effects on the whole population. Fixed effects estimation of equations (10) and (5): �(τ ) = δ τ + p β τ . Standard errors are clustered at the municipal level. All regressions control for the reproductive number R 0 , month and day of the week effects, and a first and second lockdown dummy. N = 3636 observations.  www.nature.com/scientificreports/ of Loneliness, Stress, Worry, and Frustration in the population are, even though the t-test for Frustration barely exceeds a level of one. Interestingly, for Irritability and Sleep, the estimated R 0 , coefficient is negative and highly significant. However, during high R 0 episodes, the government imposes more stringent measures to control the pandemic, so there are several confounding factors that might be affecting the social well-being. The estimated coefficient for the second lockdown dummy indicates heterogeneity among the topics. During the second lockdown, people pay more attention and respond more intensively to topics related to Stress, Worry, and Frustration. Interestingly, people are less bored and less irritable during their second lockdown than during their first experience.

Conclusions
We have estimated the effect of the implementations of lockdowns on the well-being and mental health of the Chilean population. We measure this effect by the changes in the volume of searches for keywords in Google Trends (GT) that are related to various topics: Boredom, Loneliness, Irritability, Panic, Sleep, Stress, Worry, Frustration, and Self-care. For this purpose, we exploit both the wide historical availability of GT data and especially the characteristics of the Chilean government's response to the COVID-19 pandemic (the Dynamic Quarantine). In our sample, the government imposes weekly lockdowns on the population of some municipalities and lifts some from others that is determined by the authority's evaluation of their epidemiological situation. Some municipalities were even subject to up to two distinct lockdowns during our sample period. The time and cross-sectional variation in the lockdowns provides us with the unique opportunity to estimate the population's responses as differentiated by the socioeconomic status (SES) of the municipalities.
Perhaps unsurprisingly, lockdowns can have statistically significant and persistent effects on mental health. More interesting, we find strong evidence of SES induced heterogeneity in the population's response to lockdown announcements: assuming that people carry out internet searches according to their mood, the population is more bored and more frustrated during lockdowns than during non-lockdown periods in which the levels of Boredom and Frustration are significantly lower for the population living in wealthy municipalities. On the other hand, the results also indicate that the population living in wealthy municipalities feel less lonely, less worried, and get less stressed during lockdowns. However, they do appear to experience higher levels of Irritability than the population from non-wealthy locations under lockdown. Finally, we find (weak) evidence that the population in wealthy municipalities is more concerned about Self-care during lockdowns, while there are no significant differences in the attention to Panic in GT searches by SES.
Our results indicate that SES heterogeneity should be accounted for in the design of the public policies aimed at providing support to individuals facing mental health difficulties triggered by the stringency of the measures taken to face the pandemic COVID-19. Neglecting such heterogeneity may lead to misleading conclusions about the size of the responses that are different for different SES, or the need to support certain segments of the population. Targeted public health responses must be implemented to address specific segments of the population with different mental health support needs. Although this issue may be of secondary importance for many countries or may seem difficult to implement, it should be kept in mind that municipalities are the smallest administrative units in the country, each with local health centers that can implement specific health policies.